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Suji (view source)

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==Basic Theory==
==Basic Theory==
A tile is safer against an opponent ''if'' they've discarded every type of tile (of the same suit) within an interval of three from your tile.
A tile is safer against an opponent ''if'' every same-suit tile in an interval of 3 is [[genbutsu]] <small>(100% safe due to [[furiten]])</small> against that opponent.
 
As a reminder, a tile is genbutsu if it was discarded by that opponent, if that opponent has declared riichi and then does not call [[ron]] that tile. In addition,


In other words:
In other words:
* With a 1/2/3 or 7/8/9 tile: if an opponent has discarded a tile that is 3 away, that tile is safer.
* If you have a 1/2/3 or 7/8/9 tile, and the tile that is 3-away is 100% safe, your tile is safer.
* With a 4/5/6 tile: if an opponent has discarded two different tiles that are 3 away, that tile is safer.
* If you have a 4/5/6 tile, and both types of tiles that are 3 away are 100% safe, your tile is safer.


For example, if an opponent had discarded a 4, then both 1 and 7 of the same suit are safer. If an opponent discarded both 1 and 7, then the 4 becomes safer. (If an opponent had only discarded a 1, the 4 is safer than normal, but still relatively dangerous.)
For example, if an opponent had discarded a 4, then both 1 and 7 of the same suit are safer. If an opponent discarded both 1 and 7, then the 4 becomes safer. (If an opponent had only discarded a 1, the 4 is still safer than normal, but still relatively dangerous.)


===Why suji works===
===Why suji works===
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* The most common type of wait is an open wait, which appears in ~50% of all winning hands, and ~58% of all [[riichi]] hands.<ref>Riichi hands: https://docs.google.com/spreadsheets/d/1x1CYlIPYTeOodGY4bmPevlbyeZOIcmHICcQaoSjHJEk/edit?gid=295861978#gid=295861978</ref>
* The most common type of wait is an open wait, which appears in ~50% of all winning hands, and ~58% of all [[riichi]] hands.<ref>Riichi hands: https://docs.google.com/spreadsheets/d/1x1CYlIPYTeOodGY4bmPevlbyeZOIcmHICcQaoSjHJEk/edit?gid=295861978#gid=295861978</ref>
* [[Sequence]]s are comprised of three sequential tiles, so an open wait always will win off two tiles that are 3-apart. For example, a {23} ryanmen can win off either a 1 or 4 of the same suit. {34} can win off a 2 or 5 of the same suit. This continues until you get the intervals of: 1-4, 4-7, 2-5, 5-8, 3-6, and 6-9.
* [[Sequence]]s are comprised of three sequential tiles, so an open wait always will win off two tiles that are 3-apart. For example, a {23} ryanmen can win off either a 1 or 4 of the same suit. {34} can win off a 2 or 5 of the same suit. This continues until you get the intervals of: 1-4, 4-7, 2-5, 5-8, 3-6, and 6-9.
* Due to the [[furiten]] rule, if a player has previously discarded any tile they could have won off of, they cannot win from other players.
* If a player is affected by [[furiten]], they become unable to ron ''any'' tile. For example, if an opponent discards a 1, and waits on 1-4, they cannot ron 4. Therefore, if every tile in a suji interval is discarded, then the other tile in that interval become safer against that player. Genbutsu tiles are those that cause furiten, so tiles 3 away from genbutsu are safer than normal.
* Therefore, if every tile in a suji interval is discarded, then the other tile in that interval become safer against that player.  
** If an opponent discards a 4, it is ''impossible'' for an opponent to have an open wait on 1 (without being in furiten). There is only one interval for the 1, that being 1-4, which is eliminated. Therefore, the 1 is safer against that opponent. Likewise, the 7 becomes safer when a 4 is discarded, due to the 4-7 interval being impossible.
** If an opponent discards a 4, it is ''impossible'' for an opponent to have an open wait on 1 (without being in furiten). There is only one interval for the 1, that being 1-4, which is eliminated. Therefore, the 1 is safer against that opponent. Likewise, the 7 becomes safer when a 4 is discarded, due to the 4-7 interval being impossible.
** If an opponent discards a 1, it is not impossible for an opponent to have an open wait on 4. There are two different intervals for 4: 1-4 and 4-7. After discarding a 1, an opponent could still have an open wait on 4-7 interval. In order for the 4 to be a "full" suji, both 1 and 7 have to be discarded. The same logic applies to tiles numbered 5 and 6.
** If an opponent discards a 1, it is not impossible for an opponent to have an open wait on 4. There are two different intervals for 4: 1-4 and 4-7. After discarding a 1, an opponent could still have an open wait on 4-7 interval. In order for the 4 to be a "full" suji, both 1 and 7 have to be discarded. The same logic applies to tiles numbered 5 and 6.
Note: suji applies to the other forms of furiten, not just discard furiten. So long as a tile is [[genbutsu]] (an opponent would be furiten if they were waiting on that tile), then the tiles within "suji interval" of that tile are safe. Most importantly: after an opponent declares [[riichi]], then any non-winning tile discarded by anyone becomes safe through furiten. Therefore, suji can also be applied to those discarded tiles. So if an opponent declares riichi, and the next opponent discards a 4, then 1 and 7 are considered suji against the riichi-declarer.


==Intervals==
==Intervals==
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